Omni is licensed under the Busines Source License 1.1 which is not an open source license. Omni is a “source available” license which allows you to run Omni in non-production environments without a business agreement with Sidero Labs.
Yes, Omni and the rest of the Sidero Stack can be run without internet access.
To do so you will need to run each component within your environment.Please see documents: